NCERT Class 8 Maths Chapter 2
Power Play
NCERT Class 8 Maths Chapter 2 (Ganita Prakash) explores powers and exponents — the compact notation for representing very large and very small numbers. This CBSE chapter covers laws of exponents, negative exponents, zero exponent, and standard form (scientific notation). Students learn to simplify expressions involving powers and understand applications in science and technology where extreme numbers appear.
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Key Terms
- Exponent (Power)
- A number written as a superscript indicating how many times the base is multiplied by itself; in aⁿ, n is the exponent and a is the base.
- Base
- The number being multiplied repeatedly in an exponential expression; in 2⁵, the base is 2.
- Standard Form
- A way of writing very large or very small numbers as a product of a number between 1 and 10 and a power of 10; also called scientific notation; e.g., 3,000,000 = 3 × 10⁶.
- Negative Exponent
- An exponent that is a negative number; a⁻ⁿ = 1/aⁿ; e.g., 2⁻³ = 1/8. Used to represent very small numbers in standard form.
- Zero Exponent
- Any non-zero number raised to the power zero equals 1; a⁰ = 1 (where a ≠ 0).
- Laws of Exponents
- Rules for simplifying expressions with exponents: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, (ab)ⁿ = aⁿbⁿ.
- Comparing Large Numbers
- Using powers of 10 and standard form to compare very large quantities, such as the population of a country or the distance between stars.
Frequently Asked Questions
What are the laws of exponents Class 8 Maths?▾
The main laws of exponents for Class 8 are: (1) aᵐ × aⁿ = aᵐ⁺ⁿ (multiply — add powers), (2) aᵐ ÷ aⁿ = aᵐ⁻ⁿ (divide — subtract powers), (3) (aᵐ)ⁿ = aᵐⁿ (power of a power — multiply), (4) (ab)ⁿ = aⁿbⁿ, (5) (a/b)ⁿ = aⁿ/bⁿ, (6) a⁰ = 1, (7) a⁻ⁿ = 1/aⁿ.
What is standard form (scientific notation) Class 8 NCERT?▾
Standard form (scientific notation) expresses a number as m × 10ⁿ where 1 ≤ m < 10 and n is an integer. Examples: 5,800,000 = 5.8 × 10⁶; 0.00042 = 4.2 × 10⁻⁴. It is used in science to write very large numbers (like distances in space) or very small numbers (like the size of atoms) concisely.
What is a negative exponent Class 8?▾
A negative exponent means the reciprocal of the positive exponent: a⁻ⁿ = 1/aⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125; 10⁻⁴ = 1/10,000 = 0.0001. Negative exponents are used in scientific notation to represent very small numbers.
Why does anything to the power zero equal 1 Class 8?▾
Using the law aᵐ ÷ aⁿ = aᵐ⁻ⁿ: when m = n, aⁿ ÷ aⁿ = aⁿ⁻ⁿ = a⁰. But any number divided by itself equals 1. Therefore a⁰ = 1 (for any non-zero a). This is not just a rule to memorise — it follows logically from the laws of exponents.
How do you simplify expressions with exponents Class 8 Maths?▾
Apply the laws of exponents step by step: (1) If multiplying same base, add powers: 3⁴ × 3² = 3⁶. (2) If dividing same base, subtract powers: 5⁷ ÷ 5³ = 5⁴. (3) Power of a power, multiply: (2³)⁴ = 2¹². (4) Simplify negative exponents: 4⁻² = 1/16. Always work with the same base where possible.
Where are exponents used in real life Class 8?▾
Exponents are used everywhere: in science (speed of light = 3×10⁸ m/s; size of an atom = 10⁻¹⁰ m), in computing (a computer with 2³² possible memory addresses), in finance (compound interest calculations), and in measuring earthquakes (the Richter scale is logarithmic, based on powers of 10).
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